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Mathematical Problems in Engineering
Volume 2016, Article ID 8673809, 13 pages
Research Article

Explicit Determinantal Representation Formulas of -Weighted Drazin Inverse Solutions of Some Matrix Equations over the Quaternion Skew Field

Pidstrygach Institute for Applied Problems of Mechanics and Mathematics, NAS of Ukraine, Lviv 79060, Ukraine

Received 25 January 2016; Accepted 24 April 2016

Academic Editor: Romain Aubry

Copyright © 2016 Ivan I. Kyrchei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


By using determinantal representations of the -weighted Drazin inverse previously obtained by the author within the framework of the theory of the column-row determinants, we get explicit formulas for determinantal representations of the -weighted Drazin inverse solutions (analogs of Cramer’s rule) of the quaternion matrix equations , , and .